Please help. How do I solve an equation with just variables

Question

Here are two of my equations

 

 

mx + nx = y

 

a= w - y

         r

Answer 1

Read my comment first, please.

 

For the first one, we'll guess that we're supposed to solve it for x. We could be asked to solve it for m or for n, so I can't be sure.

To solve it for x means to get x by itself on one side of the equals sign, and everything else on the other side, just as it does in equations with only one variable. The steps are mostly the same, but simplifying is very different.

 

For this one, we notice that x appears twice, and that it appears in every term on the left side of the equation. Because x is in every term, we can factor it out of the left side, getting:

 

x(m+n) = y     Make sure you're clear on that before you read any further.

 

Now, our goal is to get x by itself. What is preventing that is the (m+n) that is being multiplied by the x. How do we undo a multiplication? By dividing, so we divide both sides of the equation by  (m+n)  (since that is what we need to get out of there)

 

This gives us    x = y/(m+n) and we're finished.

 

 

In the other one, you could be solving it for w or for y or for r, so we should wait until you have the complete question before attacking it.